We study Manin triples for a reductive Lie algebra, g. First, we generalize results of E. Karolinsky, on the classification of Lagrangian subalgebras (cf. KAROLINSKY E., A Classification of Poisson homogeneous spaces of a compact Poisson Lie group, Dokl. Ak. Nauk, 359 (1998), 13-15). Then we show that, if g is non commutative, one can attach , to each Manin triple in g , another one for a stric...

BACKGROUND The use of an oscillating saw for cast removal creates a potential for iatrogenic injury and patient discomfort. Burns and abrasions can occur from the heat created by frictional forces and direct blade contact. With use of a cadaver model system, skin temperature measurements were recorded during cast removal with an oscillating saw. METHODS Casts of uniform thickness were applied...

toriyeh means concealing real intention of speech using its parallel and common words so that the listener constructs from speaker's speech a meaning what he/she meant. the purpose of this research is studying jurisprudential dimensions of toriyeh in order to clarify its distinction from lying and related jurisprudential commandments by explanation of the most important discussions about t...

locally extended affine lie algebras were introduced by morita and yoshii in [j. algebra 301(1) (2006), 59-81] as a natural generalization of extended affine lie algebras. after that, various generalizations of these lie algebras have been investigated by others. it is known that a locally extended affine lie algebra can be recovered from its centerless core, i.e., the ideal generated by weight...

I offer the first sustained defence of claim that ugliness is constituted by disposition to disgust. advance three main lines argument in support this thesis. First, and disgustingness tend lie same kinds things properties (the from ostensions). Second, thesis better placed than all existing accounts accommodate following facts: narrowly systematically distributed a heterogenous set things, som...

We describe the isomorphism classes of infinite-dimensional graded Lie algebras of maximal class over fields of odd characteristic.

In order to describe non-Hamiltonian (dissipative) systems in quantum theory we need to use non-Lie algebra such that commutators of this algebra generate Lie subalgebra. It was shown that classical connection between analytic group (Lie group) and Lie algebra, proved by Lie theorems, exists between analytic loop, commutant of which is associative subloop (group), and commutant Lie algebra (an ...

Although the ideas date back to the early nineteenth century (see [1; Chapter 5] for detailed historical remarks), the theory of moving frames (“repères mobiles”) is most closely associated with the name of Élie Cartan, [12], who molded it into a powerful and algorithmic tool for studying the geometric properties of submanifolds and their invariants under the action of a transformation group. I...

where tE:R and I is the unit matrix of degree d. Let GL(K, d) denote the group of all nonsingular matrices of degree d with coefficients in K. Any subgroup of GL(K, d) will be called a linear group of degree d. Let 0 be the identity representation of a linear Lie group G with the Lie algebra 8 so that 9(x) =x (*EG). Then dd is a faithful representation of g and exp dd(X) =0(exp X) =exp X for an...